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Eigenvalues And Weights Of Induced Subgraphs
, 1999
"... We apply eigenvalue techniques for cut evaluation to produce relations between the weight and order of induced subgraphs, and apply these results to bound the stability number. ..."
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We apply eigenvalue techniques for cut evaluation to produce relations between the weight and order of induced subgraphs, and apply these results to bound the stability number.
Eigenvalue conditions for induced subgraphs
"... Abstract Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented. ..."
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Abstract Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.
Induced Subgraphs of Johnson Graphs
, 2006
"... The Johnson graph J(n, N) is defined as the graph whose vertices are the nsubsets of the set {1, 2, · · · , N}, where two vertices are adjacent if they share exactly n−1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. W ..."
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The Johnson graph J(n, N) is defined as the graph whose vertices are the nsubsets of the set {1, 2, · · · , N}, where two vertices are adjacent if they share exactly n−1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before
Induced Subgraphs With Distinct Sizes
, 2009
"... We show that for every 0 <ɛ<1/2, there is an n0 = n0(ɛ) such that if n> n0 then every nvertex graph G of size at least ɛ ( ) () n n and at most (1 − ɛ) contains induced kvertex 2 2 subgraphs with at least 10−7k different sizes, for every k ≤ ɛn. This is best possible, up to a constant 3 ..."
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Cited by 1 (0 self)
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We show that for every 0 <ɛ<1/2, there is an n0 = n0(ɛ) such that if n> n0 then every nvertex graph G of size at least ɛ ( ) () n n and at most (1 − ɛ) contains induced kvertex 2 2 subgraphs with at least 10−7k different sizes, for every k ≤ ɛn. This is best possible, up to a constant
Detecting induced subgraphs
, 2007
"... An sgraph is a graph with two kinds of edges: subdivisible edges and real edges. A realisation of an sgraph B is any graph obtained by subdividing subdivisible edges of B into paths of arbitrary length (at least one). Given an sgraph B, we study the decision problem Î B whose instance is a graph ..."
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Cited by 13 (5 self)
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G and question is âDoes G contain a realisation of B as an induced subgraph?â. For several Bâs, the complexity of Î B is known and here we give the complexity for several more. Our NPcompleteness proofs for Î Bâs rely on the NPcompleteness proof of the following problem. Let S be a set
Sizes of induced subgraphs of Ramsey graphs
, 2008
"... An nvertex graph G is cRamsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every cRamsey graph with n vertices contains Ω(n 5/2) induced subgraphs any two of which differ either in the number of vertices or i ..."
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Cited by 3 (1 self)
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An nvertex graph G is cRamsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every cRamsey graph with n vertices contains Ω(n 5/2) induced subgraphs any two of which differ either in the number of vertices
Line Graphs and Forbidden Induced Subgraphs
, 2001
"... Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell if it cons ..."
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Cited by 4 (1 self)
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Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell
Induced Subgraphs of Given SIzes
, 1998
"... We say (n, e) → (m, f), an (m, f) subgraph is forced, if every nvertex graph of size e has “ an mvertex spanned subgraph with f edges. For example, as Turán proved, (n, e) → for e> tk−1(n) and (n, e) ̸→, otherwise. We give a number of k, ` k 2 k, ` k 2 constructions showing that forced pairs ..."
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Cited by 1 (0 self)
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We say (n, e) → (m, f), an (m, f) subgraph is forced, if every nvertex graph of size e has “ an mvertex spanned subgraph with f edges. For example, as Turán proved, (n, e) → for e> tk−1(n) and (n, e) ̸→, otherwise. We give a number of k, ` k 2 k, ` k 2 constructions showing that forced
Results 1  10
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1,399